Dear Dr. Abdolrasoul Ranjbaran

Thank you for this interesting idea for solving probabilistic problems. Here are my concerns that may be helpful:

1. It seems that the proposed approach is developed for solving specific probabilistic problems (i.e. fragility curves) and it is not a general probabilistic approach as Monte Carlo simulation (MCS). For example, I use MCS to estimate rare events, solve reliability problems (Aleatory/epistemic) and obtain the moments of the output function. How I can use the proposed approach for solving mentioned problems and derive PDF of complex systems?

2. It seems that the proposed method is an intuitive approach and it is not based on strong mathematical basis. I believe that the proposed approach may be a kind of response surface methodology that fits a curve based on small input data and may not be accurate for high range of problems specially those with nonlinear functions. It may be very efficient, but in contrast with MCS, the accuracy of results is not guaranteed. You should prove the accuracy of method through strong mathematical basis. Beside, a wide range of probabilistic problems should be solved by the proposed approach (accurately and without sensitivity to the parameters of your approach) for verification purpose. Then, it may be comparable with MCS.

In summery:

Your study is highly valuable but, I believe that the proposed approach may be only efficient and accurate for solving specific probabilistic problems (noting that I have not examined your approach) and introducing it as an alternative of MCS may not be correct.

I am ready for further discussions in this regard.

Best regards,

Mohsen

Dear Dr Mohsen Rashki

Thank you very much for your response. The proposed method is quite general and is based on sound mathematical basis! But the basics were not in the note.

Perhaps the more complete note may be helpful. I am ready to discuss the subject.

I am very happy to discuss the subject with the one from your university, because I have a faculty member in Shahid Nikbakht for for more than 23 years.

best regards

Apologize for uploading the previous file again!

Here is the correct one.

23 years in USB?! Great! It is nice to be connected with you.

I will read the draft. In my last paper, I have presented a method with the accuracy of crude MCS and provided a set of examples that mainstream probabilistic approaches fail to solve them. To examine your approach, you may solve them (I can do it if you provide the Matlab code of your approach here):

Article The Soft Monte Carlo Method

Evidently if your approach solves all these examples with high accuracy, beside the crude and soft MCS, I will use/suggest your approach in my next papers.

Best regards,

Mohsen

Dear Mohsen Rashki

Thank you for your interest. Yes I downloaded your paper. I will go through it.

best regards